package service;

public class FFT {

	// compute the FFT of x[], assuming its length is a power of 2
	public static Complex[] fft(Complex[] x) {
		int N = x.length;

		// base case
		if (N == 1)
			return new Complex[] { x[0] };

		// radix 2 Cooley-Tukey FFT
		if (N % 2 != 0) {
			throw new RuntimeException("N is not a power of 2");
		}

		// fft of even terms
		Complex[] even = new Complex[N / 2];
		for (int k = 0; k < N / 2; k++) {
			even[k] = x[2 * k];
		}
		Complex[] q = fft(even);

		// fft of odd terms
		Complex[] odd = even; // reuse the array
		for (int k = 0; k < N / 2; k++) {
			odd[k] = x[2 * k + 1];
		}
		Complex[] r = fft(odd);

		// combine
		Complex[] y = new Complex[N];
		for (int k = 0; k < N / 2; k++) {
			double kth = -2 * k * Math.PI / N;
			Complex wk = new Complex(Math.cos(kth), Math.sin(kth));
			y[k] = q[k].plus(wk.times(r[k]));
			y[k + N / 2] = q[k].minus(wk.times(r[k]));
		}
		return y;
	}

	// compute the inverse FFT of x[], assuming its length is a power of 2
	public static Complex[] ifft(Complex[] x) {
		int N = x.length;
		Complex[] y = new Complex[N];

		// take conjugate
		for (int i = 0; i < N; i++) {
			y[i] = x[i].conjugate();
		}

		// compute forward FFT
		y = fft(y);

		// take conjugate again
		for (int i = 0; i < N; i++) {
			y[i] = y[i].conjugate();
		}

		// divide by N
		for (int i = 0; i < N; i++) {
			y[i] = y[i].times(1.0 / N);
		}

		return y;

	}

	// compute the circular convolution of x and y
	public static Complex[] cconvolve(Complex[] x, Complex[] y) {

		// should probably pad x and y with 0s so that they have same length
		// and are powers of 2
		if (x.length != y.length) {
			throw new RuntimeException("Dimensions don't agree");
		}

		int N = x.length;

		// compute FFT of each sequence
		Complex[] a = fft(x);
		Complex[] b = fft(y);

		// point-wise multiply
		Complex[] c = new Complex[N];
		for (int i = 0; i < N; i++) {
			c[i] = a[i].times(b[i]);
		}

		// compute inverse FFT
		return ifft(c);
	}

	// compute the linear convolution of x and y
	public static Complex[] convolve(Complex[] x, Complex[] y) {
		Complex ZERO = new Complex(0, 0);

		Complex[] a = new Complex[2 * x.length];
		for (int i = 0; i < x.length; i++)
			a[i] = x[i];
		for (int i = x.length; i < 2 * x.length; i++)
			a[i] = ZERO;

		Complex[] b = new Complex[2 * y.length];
		for (int i = 0; i < y.length; i++)
			b[i] = y[i];
		for (int i = y.length; i < 2 * y.length; i++)
			b[i] = ZERO;

		return cconvolve(a, b);
	}

	// display an array of Complex numbers to standard output
	public static void show(Complex[] x, String title) {
		System.out.println(title);
		System.out.println("-------------------");
		for (int i = 0; i < x.length; i++) {
			System.out.println(x[i]);
		}
		System.out.println();
	}

}